29.1.7 problem 6

Internal problem ID [4614]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 6
Date solved : Monday, January 27, 2025 at 09:26:19 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 44

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

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

✓ Solution by Mathematica

Time used: 0.251 (sec). Leaf size: 47

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

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