Internal problem ID [12926]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime } x=\arcsin \left (x^{2}\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 109
dsolve(x*diff(y(x),x)=arcsin(x^2),y(x), singsol=all)
\[ y = -\frac {i \arcsin \left (x^{2}\right )^{2}}{4}+\frac {\arcsin \left (x^{2}\right ) \ln \left (1+i x^{2}+\sqrt {-x^{4}+1}\right )}{2}-\frac {i \operatorname {polylog}\left (2, -i x^{2}-\sqrt {-x^{4}+1}\right )}{2}+\frac {\arcsin \left (x^{2}\right ) \ln \left (1-i x^{2}-\sqrt {-x^{4}+1}\right )}{2}-\frac {i \operatorname {polylog}\left (2, i x^{2}+\sqrt {-x^{4}+1}\right )}{2}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 56
DSolve[x*y'[x]==ArcSin[x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{4} i \left (\arcsin \left (x^2\right )^2+\operatorname {PolyLog}\left (2,e^{2 i \arcsin \left (x^2\right )}\right )\right )+\frac {1}{2} \arcsin \left (x^2\right ) \log \left (1-e^{2 i \arcsin \left (x^2\right )}\right )+c_1 \]