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 : Monday, January 27, 2025 at 09:26:12 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 58

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

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

✓ Solution by Mathematica

Time used: 0.080 (sec). Leaf size: 46

DSolve[D[y[x],x]==x^2+3*Cosh[x]+2*y[x],y[x],x,IncludeSingularSolutions -> True]
 

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