82.10.1 problem Ex. 1

Internal problem ID [18756]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 27
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:15:12 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 31

dsolve(x*diff(y(x),x)-a*y(x)=x+1,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: 0.069 (sec). Leaf size: 21

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

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