Internal problem ID [13760]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number: 43.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\left (-x^{2}+4\right )^{\frac {3}{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x)=(4-x^2)^(3/2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \left (-x^{2}+4\right )^{\frac {3}{2}}}{4}+\frac {3 \sqrt {-x^{2}+4}\, x}{2}+6 \arcsin \left (\frac {x}{2}\right )+c_{1} \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 49
DSolve[y'[x]==(4-x^2)^(3/2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -12 \arctan \left (\frac {\sqrt {4-x^2}}{x+2}\right )-\frac {1}{4} x \sqrt {4-x^2} \left (x^2-10\right )+c_1 \]