2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Differential Equations

JEE Main & Advanced Mathematics Differential Equations Question Bank Variable Separable type differential equations

  • question_answer
    The solution of differential equation \[y-x\frac{dy}{dx}=a\left( {{y}^{2}}+\frac{dy}{dx} \right)\] is    [MP PET 2002]

    A)                 \[(x+a)(x+ay)=cy\]             

    B)                 \[(x+a)(1-ay)=cy\]

    C)                 \[(x+a)(1-ay)=c\] 

    D)                 None of these

    Correct Answer: B

    Solution :

                       \[y-x\frac{dy}{dx}=a\,\left( {{y}^{2}}+\frac{dy}{dx} \right)\] Þ \[y-a{{y}^{2}}=a\frac{dy}{dx}+x\frac{dy}{dx}\]         Þ \[y(1-ay)=\left( a+x \right)\,.\frac{dy}{dx}\] Þ \[\frac{dx}{(a+x)}=\frac{dy}{y(1-ay)}\]         Integrating both sides, \[\int{\frac{dx}{(a+x)}=}\int{\frac{dy}{y(1-ay)}}\]         Þ \[\int{\frac{dx}{a+x}=\int{\left[ \frac{1}{y}+\frac{a}{(1-ay)} \right]\,dx}}\]         \[\log (a+x)=\log y+\frac{a\log (1-ay)}{-a}\]         Þ \[\log (a+x)=\log y-\log (1-ay)+\log c\]                 Þ \[\log (x+a)(1-ay)=\log cy\] Þ \[(x+a)(1-ay)=cy\].


You need to login to perform this action.
You will be redirected in 3 sec spinner