38.2.11 problem 11

Internal problem ID [6440]
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 : 11
Date solved : Monday, January 27, 2025 at 02:04:13 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 21

dsolve(x*diff(y(x),x)-y(x)=x^3+3*x^2-2*x,y(x), singsol=all)
 

\[ y = \frac {\left (x^{2}+6 x -4 \ln \left (x \right )+2 c_1 \right ) x}{2} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 24

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

\[ y(x)\to x \left (\frac {x^2}{2}+3 x-2 \log (x)+c_1\right ) \]