38.2.34 problem 34

Internal problem ID [6463]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 34
Date solved : Monday, January 27, 2025 at 02:06:12 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+2 y&=3 x -1 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 12

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

\[ y = x -\frac {1}{2}-\frac {2}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 15

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

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