7.5.39 problem 39

Internal problem ID [143]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 39
Date solved : Friday, February 07, 2025 at 07:57:29 AM
CAS classification : [_exact, _rational]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

dsolve(( 3*x^2*y(x)^3 + y(x)^4)+( 3*x^3*y(x)^2 + y(x)^4+4*x*y(x)^3 )*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y^{4} x +x^{3} y^{3}+\frac {y^{5}}{5}+c_1 &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 32.434 (sec). Leaf size: 171

DSolve[( 3*x^2*y[x]^3+y[x]^4)+(3*x^3*y[x]^2+y[x]^4+4*x*y[x]^3 )*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 0 \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,1\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,2\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,3\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,4\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,5\right ] \\ y(x)\to 0 \\ \end{align*}