64.4.17 problem 17

Internal problem ID [13306]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 05:17:26 AM
CAS classification : [_separable]

\begin{align*} \left (3 x +8\right ) \left (y^{2}+4\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.063 (sec). Leaf size: 21

dsolve([(3*x+8)*(y(x)^2+4)-4*y(x)*(x^2+5*x+6)*diff(y(x),x)=0,y(1) = 2],y(x), singsol=all)
 

\[ y = \frac {2 \sqrt {-9+\left (3 x +6\right ) \sqrt {x +3}}}{3} \]

✓ Solution by Mathematica

Time used: 5.247 (sec). Leaf size: 48

DSolve[{(3*x+8)*(y[x]^2+4)-4*y[x]*(x^2+5*x+6)*D[y[x],x]==0,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 \sqrt {2 \exp \left (2 \int _1^x\frac {3 K[1]+8}{4 \left (K[1]^2+5 K[1]+6\right )}dK[1]\right )-1} \]