Internal problem ID [3870]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 22
Problem number: 622.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {\left (y+3 x \right )^{2} y^{\prime }-4 \left (3 x +2 y\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 47
dsolve((3*x+y(x))^2*diff(y(x),x) = 4*(3*x+2*y(x))*y(x),y(x), singsol=all)
\[ 3 \ln \left (\frac {y \left (x \right )}{x}\right )-3 \ln \left (-\frac {-y \left (x \right )+3 x}{x}\right )-\ln \left (\frac {x +y \left (x \right )}{x}\right )-\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 60.159 (sec). Leaf size: 747
DSolve[(3 x+y[x])^2 y'[x]==4(3 x+2 y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}-\sqrt {2} \sqrt {-6 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}-48 x^2+\frac {\left (-8 x+e^{c_1}\right ){}^3-72 x^2 \left (-8 x+e^{c_1}\right )}{\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}}+\left (-8 x+e^{c_1}\right ){}^2}+8 x-e^{c_1}\right ) y(x)\to \frac {1}{4} \left (-\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}+\sqrt {2} \sqrt {-6 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}-48 x^2+\frac {\left (-8 x+e^{c_1}\right ){}^3-72 x^2 \left (-8 x+e^{c_1}\right )}{\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}}+\left (-8 x+e^{c_1}\right ){}^2}+8 x-e^{c_1}\right ) y(x)\to \frac {1}{4} \left (\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}-\sqrt {2} \sqrt {-6 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}-48 x^2+\frac {72 x^2 \left (-8 x+e^{c_1}\right )-\left (-8 x+e^{c_1}\right ){}^3}{\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}}+\left (-8 x+e^{c_1}\right ){}^2}+8 x-e^{c_1}\right ) y(x)\to \frac {1}{4} \left (\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}+\sqrt {2} \sqrt {-6 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}-48 x^2+\frac {72 x^2 \left (-8 x+e^{c_1}\right )-\left (-8 x+e^{c_1}\right ){}^3}{\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}}+\left (-8 x+e^{c_1}\right ){}^2}+8 x-e^{c_1}\right ) \end{align*}