10.2.37 problem 38

Internal problem ID [1165]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 38
Date solved : Monday, January 27, 2025 at 04:37:44 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y^{\prime }&=\frac {3 y^{2}-x^{2}}{2 y x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

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

\begin{align*} y &= \sqrt {c_1 x +1}\, x \\ y &= -\sqrt {c_1 x +1}\, x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.223 (sec). Leaf size: 34

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

\begin{align*} y(x)\to -x \sqrt {1+c_1 x} \\ y(x)\to x \sqrt {1+c_1 x} \\ \end{align*}