73.4.28 problem 5.4 (b)

Internal problem ID [15110]
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)
Date solved : Tuesday, January 28, 2025 at 07:31:07 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (2\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.059 (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)
 

\[ y = \frac {\sqrt {\pi }\, \sqrt {2}\, \operatorname {FresnelS}\left (\frac {\sqrt {2}\, \sqrt {x}}{\sqrt {\pi }}\right )+10-\sqrt {\pi }\, \sqrt {2}\, \operatorname {FresnelS}\left (\frac {2}{\sqrt {\pi }}\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.078 (sec). Leaf size: 185

DSolve[{x^2*D[y[x],x]+x*y[x]==Sqrt[x]*Sin[x],{y[2]==5}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 i \sqrt {\pi } x \text {erf}\left (\sqrt {i x}\right )-(1+i) \sqrt {2 \pi } \text {erf}(1+i) \sqrt {i x} \sqrt {x}-2 i \sqrt {\pi } x \text {erfi}\left (\sqrt {i x}\right )+(1+i) \sqrt {2 \pi } \text {erfi}(1+i) \sqrt {i x} \sqrt {x}-2 \sqrt {\pi } \sqrt {x^2}-2 i \sqrt {\pi } x+2 \sqrt {2 \pi } \sqrt {i x} \sqrt {x}+40 \sqrt {i x} \sqrt {x}}{4 \sqrt {i x} x^{3/2}} \]