29.6.7 problem 153

Internal problem ID [4753]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 153
Date solved : Monday, January 27, 2025 at 09:36:27 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=1+x +a y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 31

dsolve(x*diff(y(x),x) = 1+x+a*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (-\frac {x^{-a} \left (a x +a -1\right )}{a \left (a -1\right )}+c_{1} \right ) x^{a} \]

✓ Solution by Mathematica

Time used: 1.123 (sec). Leaf size: 28

DSolve[x D[y[x],x]==1+x+a y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {a x+a-1}{(a-1) a}+c_1 x^a \]