67.2.7 problem Problem 1(g)

Internal problem ID [13893]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 1(g)
Date solved : Monday, March 31, 2025 at 08:16:35 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 36

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

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

✓ Mathematica. Time used: 0.161 (sec). Leaf size: 66

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

\[ y(x)\to \exp \left (\int _1^x-e^{K[1]^2} \sec (K[1])dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}-e^{K[1]^2} \sec (K[1])dK[1]\right ) \sec (K[2]) \sinh (K[2])dK[2]+c_1\right ) \]

✗ Sympy

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

Timed Out