+91-93193 64476
FlagBACK
Flag Integral Calculus> differential equation...
question mark

form the differential equation for the following family of curves y=c1*(e^x)+(e^c1)*e^(2x)+(ln(c1))*e^(3x)

pratik mohanty , 13 Years ago
Grade 12th Pass
anser 1 Answers
Jitender Singh
Ans:
y = c_{1}e^{x} + e^{c_{1}}e^{2x} + lnc_{1}.e^{3x}
y' = c_{1}e^{x} + 2e^{c_{1}}e^{2x} + 3 lnc_{1}.e^{3x}
y'' = c_{1}e^{x} + 4e^{c_{1}}e^{2x} + 9lnc_{1}.e^{3x}
y''' = c_{1}e^{x} + 8e^{c_{1}}e^{2x} + 27lnc_{1}.e^{3x}
Differential equation of family of curves:
You can solve this system of equations by matrix method. Matrix would be of 4 columns & 4 rows.
First column elements will be 1, 1, 1 & 1, second column elements will be 1, 2, 4 & 8, third column will be 1, 3, 9 & 27 ans 4thcolumn will be y, y’, y’’ & y’’’.
Detrminent of matrix is zero.
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty
Last Activity: 11 Years ago
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Other Related Questions on integral calculus

question mark
The area of a square field is 640000cm2.what is its area in hectares
integral calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
Please solve this integration. I am facing difficulty in it
 How to solve this. Please solve anyone. Humble request
integral calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0
integral calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
If 4th term of an A.p is zero, show that the 8th term is double the 6th term
 
integral calculus
1 Answer Available

Last Activity: 4 Years ago