29.22.15 problem 623

Internal problem ID [5215]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 22
Problem number : 623
Date solved : Monday, January 27, 2025 at 10:21:47 AM
CAS classification : [[_homogeneous, `class C`], _rational]

\begin{align*} \left (1-3 x -y\right )^{2} y^{\prime }&=\left (1-2 y\right ) \left (3-6 x -4 y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.309 (sec). Leaf size: 75

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)
 

\[ -4 \ln \left (2\right )-\ln \left (\frac {-3 y \left (x \right )+2-3 x}{6 x -1}\right )-3 \ln \left (\frac {3 x -y \left (x \right )}{6 x -1}\right )+3 \ln \left (\frac {1-2 y \left (x \right )}{6 x -1}\right )-\ln \left (6 x -1\right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 60.197 (sec). Leaf size: 1089

DSolve[(1-3 x-y[x])^2 D[y[x],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*}