15.3.16 problem 16

Internal problem ID [2909]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 7, page 28
Problem number : 16
Date solved : Monday, January 27, 2025 at 06:53:02 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✗ Solution by Maple

dsolve([(3*x-y(x)+2)+(x+2*y(x)+1)*diff(y(x),x)=0,y(0) = 0],y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.189 (sec). Leaf size: 111

DSolve[{(3*x-y[x]+2)+(x+2*y[x]+1)*D[y[x],x]==0,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \sqrt {6} \arctan \left (\frac {\sqrt {\frac {2}{3}} (-y(x)+3 x+2)}{2 y(x)+x+1}\right )=3 \left (\frac {2}{3} \left (\sqrt {6} \arctan \left (2 \sqrt {\frac {2}{3}}\right )+3 \log \left (\frac {25}{22}\right )-6 \log (5)\right )+2 \log \left (\frac {42 x^2+28 y(x)^2+8 y(x)+60 x+22}{(7 x+5)^2}\right )+4 \log (7 x+5)\right ),y(x)\right ] \]