Internal problem ID [13347]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {x^{2} y^{\prime }+3 x^{2} y=\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 60
dsolve(x^2*diff(y(x),x)+3*x^2*y(x)=sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {3 \left (\left (-\frac {1}{3}+i\right ) x \,\operatorname {expIntegral}_{1}\left (\left (-3-i\right ) x \right )+\left (-\frac {1}{3}-i\right ) x \,\operatorname {expIntegral}_{1}\left (\left (-3+i\right ) x \right )-\frac {i {\mathrm e}^{\left (3-i\right ) x}}{3}+\frac {i {\mathrm e}^{\left (3+i\right ) x}}{3}+\frac {2 c_{1} x}{3}\right ) {\mathrm e}^{-3 x}}{2 x} \]
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 68
DSolve[x^2*y'[x]+3*x^2*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-3 x} \left ((1+3 i) \operatorname {ExpIntegralEi}((3-i) x)+\frac {(1-3 i) x \operatorname {ExpIntegralEi}((3+i) x)-i e^{(3-i) x}+i e^{(3+i) x}+2 c_1 x}{x}\right ) \]