73.4.1 problem 5.1 (a)

Internal problem ID [15083]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.1 (a)
Date solved : Tuesday, January 28, 2025 at 07:30:09 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 46

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

\[ y = \frac {3 \,{\mathrm e}^{-3 x} \left (\left (-\frac {1}{3}+i\right ) x \,\operatorname {Ei}_{1}\left (\left (-3-i\right ) x \right )+\left (-\frac {1}{3}-i\right ) x \,\operatorname {Ei}_{1}\left (\left (-3+i\right ) x \right )-\frac {i {\mathrm e}^{\left (3-i\right ) x}}{3}+\frac {i {\mathrm e}^{\left (3+i\right ) x}}{3}+\frac {2 c_{1} x}{3}\right )}{2 x} \]

✓ Solution by Mathematica

Time used: 0.078 (sec). Leaf size: 35

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

\[ y(x)\to e^{-3 x} \left (\int _1^x\frac {e^{3 K[1]} \sin (K[1])}{K[1]^2}dK[1]+c_1\right ) \]