Internal problem ID [13374]
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: 5.4 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x^{2} y^{\prime }+y x=\sqrt {x}\, \sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (2\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 42
dsolve([x^2*diff(y(x),x)+x*y(x)=sqrt(x)*sin(x),y(2) = 5],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sqrt {\pi }\, \sqrt {2}\, \operatorname {FresnelS}\left (\frac {\sqrt {2}\, \sqrt {x}}{\sqrt {\pi }}\right )+10-\sqrt {\pi }\, \sqrt {2}\, \operatorname {FresnelS}\left (\frac {2}{\sqrt {\pi }}\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 185
DSolve[{x^2*y'[x]+x*y[x]==Sqrt[x]*Sin[x],{y[2]==5}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 i \sqrt {\pi } x \text {erf}\left (\sqrt {i x}\right )-(1+i) \sqrt {2 \pi } \text {erf}(1+i) \sqrt {i x} \sqrt {x}-2 i \sqrt {\pi } x \text {erfi}\left (\sqrt {i x}\right )+(1+i) \sqrt {2 \pi } \text {erfi}(1+i) \sqrt {i x} \sqrt {x}-2 \sqrt {\pi } \sqrt {x^2}-2 i \sqrt {\pi } x+2 \sqrt {2 \pi } \sqrt {i x} \sqrt {x}+40 \sqrt {i x} \sqrt {x}}{4 \sqrt {i x} x^{3/2}} \]