73.3.20 problem 4.5 (d)

Internal problem ID [15054]
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)
Date solved : Tuesday, January 28, 2025 at 07:28:54 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime } y&=3 \sqrt {x y^{2}+9 x} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 1.211 (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)
 

\[ y = 2 \sqrt {x^{{3}/{2}} \left (x^{{3}/{2}}+3\right )} \]

✓ Solution by Mathematica

Time used: 0.272 (sec). Leaf size: 44

DSolve[{y[x]*D[y[x],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*}