29.1.3 problem 2

Internal problem ID [4610]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 2
Date solved : Sunday, March 30, 2025 at 03:30:20 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=x^{2}+3 \cosh \left (x \right )+2 y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 58

ode:=diff(y(x),x) = x^2+3*cosh(x)+2*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{2 x} \left (\left (x^{2}+\frac {1}{2}+x \right ) \cosh \left (2 x \right )+\left (-x^{2}-x -\frac {1}{2}\right ) \sinh \left (2 x \right )-2 c_1 +3 \cosh \left (x \right )-3 \sinh \left (x \right )+\cosh \left (3 x \right )-\sinh \left (3 x \right )\right )}{2} \]

✓ Mathematica. Time used: 0.08 (sec). Leaf size: 46

ode=D[y[x],x]==x^2+3*Cosh[x]+2*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {1}{4} e^{-x} \left (e^x \left (2 x^2+2 x+1\right )+6 e^{2 x}+2\right )+c_1 e^{2 x} \]

✓ Sympy. Time used: 0.162 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 - 2*y(x) - 3*cosh(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{2 x} - \frac {x^{2}}{2} - \frac {x}{2} - \sinh {\left (x \right )} - 2 \cosh {\left (x \right )} - \frac {1}{4} \]