4.1.3 \(y'(x)=x^2+2 y(x)+3 \cosh (x)\)

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

\[ \left \{ y \relax (x ) =-{\frac {{{\rm e}^{2\,x}}}{2} \left (\left ({x}^{2}+x+{\frac {1}{2}} \right ) {{\rm e}^{-2\,x}}-2\,{\it \_C1}+3\,\cosh \relax (x ) -3\,\sinh \relax (x ) +\cosh \left (3\,x \right ) -\sinh \left (3\,x \right ) \right ) } \right \} \] 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)