62.4.2 problem Ex 2

Internal problem ID [12814]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 11. Equations in which M and N are linear but not homogeneous. Page 16
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 04:24:26 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.072 (sec). Leaf size: 36

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

\[ y = -2+\tan \left (\operatorname {RootOf}\left (2 \ln \left (2\right )+\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )-\textit {\_Z} +2 \ln \left (x +1\right )+2 c_{1} \right )\right ) \left (-2 x -2\right ) \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 67

DSolve[(4*x-y[x]+2)+(x+y[x]+3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \arctan \left (\frac {1}{2}-\frac {5 (x+1)}{2 (y(x)+x+3)}\right )+2 \log \left (\frac {4 x^2+y(x)^2+4 y(x)+8 x+8}{5 (x+1)^2}\right )+4 \log (x+1)+5 c_1=0,y(x)\right ] \]