83.8.5 problem 5

Internal problem ID [19131]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 01:04:44 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

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

\[ y \left (x \right ) = -4 x -1-2 \tan \left (-2 x +2 c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.166 (sec). Leaf size: 41

DSolve[D[y[x],x]==(4*x+y[x]+1)^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -4 x+\frac {1}{c_1 e^{4 i x}-\frac {i}{4}}-(1+2 i) \\ y(x)\to -4 x-(1+2 i) \\ \end{align*}