4.1.4 \(y'(x)=a+b x+c y(x)\)

ODE
\[ y'(x)=a+b x+c y(x) \] ODE Classification

[[_linear, `class A`]]

Book solution method
Linear ODE

Mathematica
cpu = 0.012023 (sec), leaf count = 28

\[\left \{\left \{y(x)\to c_1 e^{c x}-\frac {a c+b c x+b}{c^2}\right \}\right \}\]

Maple
cpu = 0.05 (sec), leaf count = 31

\[ \left \{ y \relax (x ) ={\frac {{{\rm e}^{cx}}{\it \_C1}\,{c}^{2}+ \left (-bx-a \right ) c-b}{{c}^{2}}} \right \} \] Mathematica raw input

DSolve[y'[x] == a + b*x + c*y[x],y[x],x]

Mathematica raw output

{{y[x] -> -((b + a*c + b*c*x)/c^2) + E^(c*x)*C[1]}}

Maple raw input

dsolve(diff(y(x),x) = a+b*x+c*y(x), y(x),'implicit')

Maple raw output

y(x) = (exp(c*x)*_C1*c^2+(-b*x-a)*c-b)/c^2