80.6.10 problem 9 (d)

Internal problem ID [18574]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 33. Problems at page 91
Problem number : 9 (d)
Date solved : Tuesday, January 28, 2025 at 12:00:44 PM
CAS classification : [_separable]

\begin{align*} \frac {y^{\prime }}{x}&=y \sin \left (x^{2}-1\right )-\frac {2 y}{\sqrt {x}} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 21

dsolve(1/x*diff(y(x),x)=y(x)*sin(x^2-1)-2*y(x)/sqrt(x),y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {\cos \left (x^{2}-1\right )}{2}-\frac {4 x^{{3}/{2}}}{3}} \]

✓ Solution by Mathematica

Time used: 0.102 (sec). Leaf size: 37

DSolve[1/x*D[y[x],x]==y[x]*Sin[x^2-1]-2*y[x]/Sqrt[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{\frac {1}{6} \left (-8 x^{3/2}-3 \cos \left (1-x^2\right )\right )} \\ y(x)\to 0 \\ \end{align*}