74.1.36 problem 43

Internal problem ID [15816]
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
Date solved : Tuesday, January 28, 2025 at 08:08:05 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\left (-x^{2}+4\right )^{{3}/{2}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 32

dsolve(diff(y(x),x)=(4-x^2)^(3/2),y(x), singsol=all)
 

\[ y = \frac {\left (-x^{3}+10 x \right ) \sqrt {-x^{2}+4}}{4}+c_{1} +6 \arcsin \left (\frac {x}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 37

DSolve[D[y[x],x]==(4-x^2)^(3/2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 6 \arcsin \left (\frac {x}{2}\right )-\frac {1}{4} x \sqrt {4-x^2} \left (x^2-10\right )+c_1 \]