73.1.4 problem 2.2 (d)

Internal problem ID [14982]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.2 (d)
Date solved : Tuesday, January 28, 2025 at 07:26:13 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 83

dsolve(x*diff(y(x),x)=arcsin(x^2),y(x), singsol=all)
 

\[ y = -\frac {i \arcsin \left (x^{2}\right )^{2}}{4}+\frac {\arcsin \left (x^{2}\right ) \ln \left (1-i x^{2}-\sqrt {-x^{4}+1}\right )}{2}+\frac {\arcsin \left (x^{2}\right ) \ln \left (1+i x^{2}+\sqrt {-x^{4}+1}\right )}{2}-\frac {i \operatorname {polylog}\left (2, \left (i x^{2}+\sqrt {-x^{4}+1}\right )^{2}\right )}{4}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 25

DSolve[x*D[y[x],x]==ArcSin[x^2],y[x],x,IncludeSingularSolutions -> True]
 

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