60.1.281 problem 282

Internal problem ID [10295]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 282
Date solved : Monday, January 27, 2025 at 06:50:58 PM
CAS classification : [[_homogeneous, `class C`], _rational]

\begin{align*} \left (y+3 x -1\right )^{2} y^{\prime }-\left (2 y-1\right ) \left (4 y+6 x -3\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.274 (sec). Leaf size: 75

dsolve((y(x)+3*x-1)^2*diff(y(x),x)-(2*y(x)-1)*(4*y(x)+6*x-3)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 60.201 (sec). Leaf size: 1089

DSolve[(y[x]+3*x-1)^2*D[y[x],x]-(2*y[x]-1)*(4*y[x]+6*x-3)==0,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*}