Internal problem ID [3266]
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`]]
\[ \boxed {y^{\prime }-2 y=x^{2}+3 \cosh \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 76
dsolve(diff(y(x),x) = x^2+3*cosh(x)+2*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{2 x} \left (-2 x^{2} \cosh \left (2 x \right )+2 x^{2} \sinh \left (2 x \right )-2 x \cosh \left (2 x \right )+2 x \sinh \left (2 x \right )+2 \sinh \left (3 x \right )-2 \cosh \left (3 x \right )+6 \sinh \left (x \right )-\cosh \left (2 x \right )-6 \cosh \left (x \right )+\sinh \left (2 x \right )+4 c_{1} \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 46
DSolve[y'[x]==x^2+3*Cosh[x]+2*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{4} e^{-x} \left (e^x \left (2 x^2+2 x+1\right )+6 e^{2 x}+2\right )+c_1 e^{2 x} \]