16.1.6 problem 2(a)

Internal problem ID [3408]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 2(a)
Date solved : Monday, January 27, 2025 at 07:35:53 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(diff(y(x),x)=arcsin(x),y(x), singsol=all)
 

\[ y \left (x \right ) = x \arcsin \left (x \right )+\sqrt {-x^{2}+1}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 23

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

\[ y(x)\to x \arcsin (x)+\sqrt {1-x^2}+c_1 \]