Find the differential equation representing the family of curves y= ae^{2x}+5,where a is an arbitrary constant.

 

 

 

 
 
 
 
 

Answers (1)

given:  y= ae^{2x}+5
On differentiating w.r.t x, we get
\frac{dy}{dx}= ae^{2x}\left ( 2 \right )+0\left [ By\: chain\: rule \right ]
\Rightarrow \frac{dy}{dx}= 2ae^{2x}-\left ( i \right )
Again differentiating w.r.t  x,
\frac{d^{2}y}{dx^{2}}= 2\left ( ae^{2x}2 \right )
\Rightarrow \frac{d^{2}y}{dx^{2}}= \frac{2dy}{dx}-\left [ using\left ( i \right ) \right ]
\Rightarrow \frac{d^{2}y}{dx^{2}}-\frac{2dy}{dx}= 0 this is the required differential equation

Most Viewed Questions

Related Chapters

Preparation Products

Knockout CUET (Physics, Chemistry and Mathematics)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout CUET (Physics, Chemistry and Biology)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions