15.6.22 problem 22

Internal problem ID [2979]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 22
Date solved : Monday, January 27, 2025 at 07:05:20 AM
CAS classification : [_linear]

\begin{align*} 2 y-y x -3+x y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 19

dsolve([(2*y(x)-x*y(x)-3)+x*diff(y(x),x)=0,y(1) = 1],y(x), singsol=all)
 

\[ y = \frac {-3 x -3+7 \,{\mathrm e}^{x -1}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 24

DSolve[{(2*y[x]-x*y[x]-3)+x*D[y[x],x]==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {7 e^x-3 e (x+1)}{e x^2} \]