ODE
\[ y'(x)=x^2+2 y(x)+3 \cosh (x) \] ODE Classification
[[_linear, `class A`]]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.0297104 (sec), leaf count = 46
\[\left \{\left \{y(x)\to c_1 e^{2 x}-\frac {1}{4} e^{-x} \left (e^x \left (2 x^2+2 x+1\right )+6 e^{2 x}+2\right )\right \}\right \}\]
Maple ✓
cpu = 0.079 (sec), leaf count = 43
\[ \left \{ y \left ( x \right ) =-{\frac {{{\rm e}^{2\,x}}}{2} \left ( \left ( {x}^{2}+x+{\frac {1}{2}} \right ) {{\rm e}^{-2\,x}}-2\,{\it \_C1}+3\,\cosh \left ( x \right ) -3\,\sinh \left ( x \right ) +\cosh \left ( 3\,x \right ) -\sinh \left ( 3\,x \right ) \right ) } \right \} \] Mathematica raw input
DSolve[y'[x] == x^2 + 3*Cosh[x] + 2*y[x],y[x],x]
Mathematica raw output
{{y[x] -> -(2 + 6*E^(2*x) + E^x*(1 + 2*x + 2*x^2))/(4*E^x) + E^(2*x)*C[1]}}
Maple raw input
dsolve(diff(y(x),x) = x^2+3*cosh(x)+2*y(x), y(x),'implicit')
Maple raw output
y(x) = -1/2*((x^2+x+1/2)*exp(-2*x)-2*_C1+3*cosh(x)-3*sinh(x)+cosh(3*x)-sinh(3*x))*exp(2*x)