Internal problem ID [3363]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 22
Problem number: 623.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational]
Solve \begin {gather*} \boxed {\left (1-3 x -y\right )^{2} y^{\prime }-\left (1-2 y\right ) \left (3-6 x -4 y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.095 (sec). Leaf size: 72
dsolve((1-3*x-y(x))^2*diff(y(x),x) = (1-2*y(x))*(3-6*x-4*y(x)),y(x), singsol=all)
\[ -\ln \left (-\frac {6 x -4+6 y \relax (x )}{6 x -1}\right )-3 \ln \left (\frac {-6 y \relax (x )+18 x}{6 x -1}\right )+3 \ln \left (\frac {-6 y \relax (x )+3}{6 x -1}\right )-\ln \left (6 x -1\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.173 (sec). Leaf size: 1089
DSolve[(1-3 x-y[x])^2 y'[x]==(1-2 y[x])(3-6 x-4 y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (-\sqrt {36 x^2-12 x+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x-1+e^{c_1}\right )}+1+16 e^{2 c_1}}-\frac {1}{2} \sqrt {-\frac {8 \left (-(6 x-1)^3+96 e^{2 c_1} (6 x-1)+30 e^{c_1} (1-6 x)^2+64 e^{3 c_1}\right )}{\sqrt {36 x^2-12 x+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x-1+e^{c_1}\right )}+1+16 e^{2 c_1}}}+8 \left (12 x+1+4 e^{c_1}\right ){}^2-96 \left (3 x (3 x+1)+2 e^{c_1}\right )-12\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x-1+e^{c_1}\right )}}+12 x+1+4 e^{c_1}\right ) \\ y(x)\to \frac {1}{6} \left (-\sqrt {36 x^2-12 x+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x-1+e^{c_1}\right )}+1+16 e^{2 c_1}}+\frac {1}{2} \sqrt {-\frac {8 \left (-(6 x-1)^3+96 e^{2 c_1} (6 x-1)+30 e^{c_1} (1-6 x)^2+64 e^{3 c_1}\right )}{\sqrt {36 x^2-12 x+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x-1+e^{c_1}\right )}+1+16 e^{2 c_1}}}+8 \left (12 x+1+4 e^{c_1}\right ){}^2-96 \left (3 x (3 x+1)+2 e^{c_1}\right )-12\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x-1+e^{c_1}\right )}}+12 x+1+4 e^{c_1}\right ) \\ y(x)\to \frac {1}{6} \left (\sqrt {36 x^2-12 x+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x-1+e^{c_1}\right )}+1+16 e^{2 c_1}}-\frac {1}{2} \sqrt {\frac {8 \left (-(6 x-1)^3+96 e^{2 c_1} (6 x-1)+30 e^{c_1} (1-6 x)^2+64 e^{3 c_1}\right )}{\sqrt {36 x^2-12 x+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x-1+e^{c_1}\right )}+1+16 e^{2 c_1}}}+8 \left (12 x+1+4 e^{c_1}\right ){}^2-96 \left (3 x (3 x+1)+2 e^{c_1}\right )-12\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x-1+e^{c_1}\right )}}+12 x+1+4 e^{c_1}\right ) \\ y(x)\to \frac {1}{6} \left (\sqrt {36 x^2-12 x+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x-1+e^{c_1}\right )}+1+16 e^{2 c_1}}+\frac {1}{2} \sqrt {\frac {8 \left (-(6 x-1)^3+96 e^{2 c_1} (6 x-1)+30 e^{c_1} (1-6 x)^2+64 e^{3 c_1}\right )}{\sqrt {36 x^2-12 x+16 e^{c_1} (6 x-1)+3\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x-1+e^{c_1}\right )}+1+16 e^{2 c_1}}}+8 \left (12 x+1+4 e^{c_1}\right ){}^2-96 \left (3 x (3 x+1)+2 e^{c_1}\right )-12\ 2^{2/3} \sqrt [3]{-e^{c_1} (6 x-1)^4 \left (6 x-1+e^{c_1}\right )}}+12 x+1+4 e^{c_1}\right ) \\ \end{align*}