Internal problem ID [13318]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page
90
Problem number: 4.5 (d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y y^{\prime }-3 \sqrt {y^{2} x +9 x}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.594 (sec). Leaf size: 17
dsolve([y(x)*diff(y(x),x)=3*sqrt(x*y(x)^2+9*x),y(1) = 4],y(x), singsol=all)
\[ y \left (x \right ) = 2 \sqrt {x^{\frac {3}{2}} \left (x^{\frac {3}{2}}+3\right )} \]
✓ Solution by Mathematica
Time used: 0.294 (sec). Leaf size: 44
DSolve[{y[x]*y'[x]==3*Sqrt[x*y[x]^2+9*x],{y[1]==4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \sqrt {3 x^{3/2}+x^3} \\ y(x)\to 2 \sqrt {-7 x^{3/2}+x^3+10} \\ \end{align*}