The General Solution for a linear Second Order Homogenous Differential Equations with Variable Coefficients

Abstract : The main goal in this work to find the general solution for some kind of linear second order homogenous differential equations with variable coefficients which have the general form , by using the substitution ,which transform form the above equation to Riccati equation

Impact of opioid-free analgesia on pain severity and patient satisfaction after discharge from surgery: multispecialty, prospective cohort study in 25 countries

Background: Balancing opioid stewardship and the need for adequate analgesia following discharge after surgery is challenging. This study aimed to compare the outcomes for patients discharged with opioid versus opioid-free analgesia after common surgical procedures.Methods: This international, multicentre, prospective cohort study collected data from patients undergoing common acute and elective general surgical, urological, gynaecological, and orthopaedic procedures. The primary outcomes were patient-reported time in severe pain measured on a numerical analogue scale from 0 to 100% and patient-reported satisfaction with pain relief during the first week following discharge. Data were collected by in-hospital chart review and patient telephone interview 1 week after discharge.Results: The study recruited 4273 patients from 144 centres in 25 countries; 1311 patients (30.7%) were prescribed opioid analgesia at discharge. Patients reported being in severe pain for 10 (i.q.r. 1-30)% of the first week after discharge and rated satisfaction with analgesia as 90 (i.q.r. 80-100) of 100. After adjustment for confounders, opioid analgesia on discharge was independently associated with increased pain severity (risk ratio 1.52, 95% c.i. 1.31 to 1.76; P < 0.001) and re-presentation to healthcare providers owing to side-effects of medication (OR 2.38, 95% c.i. 1.36 to 4.17; P = 0.004), but not with satisfaction with analgesia (beta coefficient 0.92, 95% c.i. -1.52 to 3.36; P = 0.468) compared with opioid-free analgesia. Although opioid prescribing varied greatly between high-income and low- and middle-income countries, patient-reported outcomes did not.Conclusion: Opioid analgesia prescription on surgical discharge is associated with a higher risk of re-presentation owing to side-effects of medication and increased patient-reported pain, but not with changes in patient-reported satisfaction. Opioid-free discharge analgesia should be adopted routinely

Global Incidence and Risk Factors Associated With Postoperative Urinary Retention Following Elective Inguinal Hernia Repair

Importance Postoperative urinary retention (POUR) is a well-recognized complication of inguinal hernia repair (IHR). A variable incidence of POUR has previously been reported in this context, and contradictory evidence surrounds potential risk factors.Objective To ascertain the incidence of, explore risk factors for, and determine the health service outcomes of POUR following elective IHR.Design, Setting, and Participants The Retention of Urine After Inguinal Hernia Elective Repair (RETAINER I) study, an international, prospective cohort study, recruited participants between March 1 and October 31, 2021. This study was conducted across 209 centers in 32 countries in a consecutive sample of adult patients undergoing elective IHR.Exposure Open or minimally invasive IHR by any surgical technique, under local, neuraxial regional, or general anesthesia.Main Outcomes and Measures The primary outcome was the incidence of POUR following elective IHR. Secondary outcomes were perioperative risk factors, management, clinical consequences, and health service outcomes of POUR. A preoperative International Prostate Symptom Score was measured in male patients.Results In total, 4151 patients (3882 male and 269 female; median [IQR] age, 56 [43-68] years) were studied. Inguinal hernia repair was commenced via an open surgical approach in 82.2% of patients (n = 3414) and minimally invasive surgery in 17.8% (n = 737). The primary form of anesthesia was general in 40.9% of patients (n = 1696), neuraxial regional in 45.8% (n = 1902), and local in 10.7% (n = 446). Postoperative urinary retention occurred in 5.8% of male patients (n = 224), 2.97% of female patients (n = 8), and 9.5% (119 of 1252) of male patients aged 65 years or older. Risk factors for POUR after adjusted analyses included increasing age, anticholinergic medication, history of urinary retention, constipation, out-of-hours surgery, involvement of urinary bladder within the hernia, temporary intraoperative urethral catheterization, and increasing operative duration. Postoperative urinary retention was the primary reason for 27.8% of unplanned day-case surgery admissions (n = 74) and 51.8% of 30-day readmissions (n = 72).Conclusions The findings of this cohort study suggest that 1 in 17 male patients, 1 in 11 male patients aged 65 years or older, and 1 in 34 female patients may develop POUR following IHR. These findings could inform preoperative patient counseling. In addition, awareness of modifiable risk factors may help to identify patients at increased risk of POUR who may benefit from perioperative risk mitigation strategies