Internal problem ID [1004]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y y^{\prime } x -3 x^{2}-4 y^{2}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (1) = \sqrt {3}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 15
dsolve([x*y(x)*diff(y(x),x)=3*x^2+4*y(x)^2,y(1) = 3^(1/2)],y(x), singsol=all)
\[ y \relax (x ) = \sqrt {4 x^{6}-1}\, x \]
✓ Solution by Mathematica
Time used: 0.645 (sec). Leaf size: 18
DSolve[{x*y[x]*y'[x]==3*x^2+4*y[x]^2,y[1]==Sqrt[3]},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \sqrt {4 x^6-1} \\ \end{align*}