87.8.7 problem 7

Internal problem ID [23361]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 65
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:40:28 PM
CAS classification : [_linear]

\begin{align*} \sin \left (x \right ) y^{\prime }+y \,{\mathrm e}^{x^{2}}&=1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 33

ode:=sin(x)*diff(y(x),x)+exp(x^2)*y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (\int {\mathrm e}^{\int {\mathrm e}^{x^{2}} \csc \left (x \right )d x} \csc \left (x \right )d x +c_1 \right ) {\mathrm e}^{\int -{\mathrm e}^{x^{2}} \csc \left (x \right )d x} \]

✓ Mathematica. Time used: 2.838 (sec). Leaf size: 63

ode=Sin[x]*D[y[x],{x,1}]+Exp[x^2]*y[x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x-e^{K[1]^2} \csc (K[1])dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}-e^{K[1]^2} \csc (K[1])dK[1]\right ) \csc (K[2])dK[2]+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*exp(x**2) + sin(x)*Derivative(y(x), (x, 2)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve y(x)*exp(x**2) + sin(x)*Derivative(y(x), (x, 2)) - 1