##### 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 = 0.194809 (sec), leaf count = 46

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

Maple
cpu = 0.078 (sec), leaf count = 80

$\left [y \left (x \right ) = {\mathrm e}^{2 x} \textit {\_C1} -\frac {{\mathrm e}^{2 x} \left (-2 x^{2} \sinh \left (2 x \right )+2 x^{2} \cosh \left (2 x \right )-2 x \sinh \left (2 x \right )+2 x \cosh \left (2 x \right )+6 \cosh \left (x \right )-6 \sinh \left (x \right )-2 \sinh \left (3 x \right )+2 \cosh \left (3 x \right )-\sinh \left (2 x \right )+\cosh \left (2 x \right )\right )}{4}\right ]$ Mathematica raw input

DSolve[y'[x] == x^2 + 3*Cosh[x] + 2*y[x],y[x],x]

Mathematica raw output

{{y[x] -> -1/4*(2 + 6*E^(2*x) + E^x*(1 + 2*x + 2*x^2))/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))

Maple raw output

[y(x) = exp(2*x)*_C1-1/4*exp(2*x)*(-2*x^2*sinh(2*x)+2*x^2*cosh(2*x)-2*x*sinh(2*x
)+2*x*cosh(2*x)+6*cosh(x)-6*sinh(x)-2*sinh(3*x)+2*cosh(3*x)-sinh(2*x)+cosh(2*x))
]