4.5.34 \((a+x) y'(x)=2 (a+x)^5+3 y(x)\)

ODE
\[ (a+x) y'(x)=2 (a+x)^5+3 y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00712026 (sec), leaf count = 21

\[\left \{\left \{y(x)\to (a+x)^3 \left (2 a x+c_1+x^2\right )\right \}\right \}\]

Maple
cpu = 0.007 (sec), leaf count = 19

\[ \left \{ y \relax (x ) = \left (2\,ax+{x}^{2}+{\it \_C1} \right ) \left (a+x \right ) ^{3} \right \} \] Mathematica raw input

DSolve[(a + x)*y'[x] == 2*(a + x)^5 + 3*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (a + x)^3*(2*a*x + x^2 + C[1])}}

Maple raw input

dsolve((a+x)*diff(y(x),x) = 2*(a+x)^5+3*y(x), y(x),'implicit')

Maple raw output

y(x) = (2*a*x+x^2+_C1)*(a+x)^3