Internal problem ID [14987]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 4. Equations with variables separable and equations reducible to them. Exercises
page 38
Problem number: 60.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-y b=a x +c} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x)=a*x+b*y(x)+c,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{b x} c_{1} b^{2}+\left (-a x -c \right ) b -a}{b^{2}} \]
✓ Solution by Mathematica
Time used: 0.105 (sec). Leaf size: 28
DSolve[y'[x]==a*x+b*y[x]+c,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {a b x+a+b c}{b^2}+c_1 e^{b x} \]