75.4.15 problem 60

Internal problem ID [16717]
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
Date solved : Tuesday, January 28, 2025 at 09:19:25 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=a x +b y+c \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

dsolve(diff(y(x),x)=a*x+b*y(x)+c,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{b x} c_{1} b^{2}+\left (-a x -c \right ) b -a}{b^{2}} \]

✓ Solution by Mathematica

Time used: 0.111 (sec). Leaf size: 35

DSolve[D[y[x],x]==a*x+b*y[x]+c,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{b x} \left (\int _1^xe^{-b K[1]} (c+a K[1])dK[1]+c_1\right ) \]