38.1.5 problem 5

Internal problem ID [6422]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Test excercise 24. page 1067
Problem number : 5
Date solved : Monday, January 27, 2025 at 02:01:13 PM
CAS classification : [_quadrature]

\begin{align*} x^{2} y^{\prime }&=x^{3} \sin \left (3 x \right )+4 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

dsolve(x^2*diff(y(x),x)=x^3*sin(3*x)+4,y(x), singsol=all)
 

\[ y = \frac {\sin \left (3 x \right )}{9}-\frac {x \cos \left (3 x \right )}{3}-\frac {4}{x}+c_1 \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 30

DSolve[x^2*D[y[x],x]==x^3*Sin[3*x]+4,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {4}{x}+\frac {1}{9} \sin (3 x)-\frac {1}{3} x \cos (3 x)+c_1 \]