62.12.14 problem Ex 15

Internal problem ID [12860]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number : Ex 15
Date solved : Tuesday, January 28, 2025 at 04:28:48 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.273 (sec). Leaf size: 45

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

\begin{align*} y &= \frac {c_{1} +\sqrt {4 x^{5}+c_{1}^{2}}}{2 x^{3}} \\ y &= \frac {c_{1} -\sqrt {4 x^{5}+c_{1}^{2}}}{2 x^{3}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.232 (sec). Leaf size: 124

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

\[ \text {Solve}\left [\int _1^x\left (\frac {2 y(x)^2}{5 \left (K[1] y(x)^2-1\right )}+\frac {4}{5 K[1]}\right )dK[1]+\int _1^{y(x)}\left (\frac {4 x K[2]}{5 \left (x K[2]^2-1\right )}-\int _1^x\left (\frac {4 K[2]}{5 \left (K[1] K[2]^2-1\right )}-\frac {4 K[1] K[2]^3}{5 \left (K[1] K[2]^2-1\right )^2}\right )dK[1]-\frac {2}{5 K[2]}\right )dK[2]=c_1,y(x)\right ] \]