Internal problem ID [2757]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-x^{2}-3 \cosh \relax (x )-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 80
dsolve(diff(y(x),x) = x^2+3*cosh(x)+2*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{2 x}-\frac {{\mathrm e}^{2 x} \left (-2 x^{2} \sinh \left (2 x \right )+2 x^{2} \cosh \left (2 x \right )-2 x \sinh \left (2 x \right )+2 x \cosh \left (2 x \right )+6 \cosh \relax (x )-6 \sinh \relax (x )-\sinh \left (2 x \right )+\cosh \left (2 x \right )-2 \sinh \left (3 x \right )+2 \cosh \left (3 x \right )\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 38
DSolve[y'[x]==x^2+3*Cosh[x]+2*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-2 x (x+1)-2 e^{-x}-6 e^x+4 c_1 e^{2 x}-1\right ) \\ \end{align*}