solution of the differential equation x dy/dx = y ln(y^2/x^2) is
Answers
e^(x u(x)) x (x (( du(x))/( dx) - 2) + u(x)) = e^(x u(x)) x u(x)
Solve for ( du(x))/( dx):
( du(x))/( dx) = 2
Integrate both sides with respect to x:
u(x) = integral2 dx = 2 x + c_1, where c_1 is an arbitrary constant.
Substitute back for v(x) = x u(x):
v(x) = x (2 x + c_1)
Substitute back for y(x) = e^v(x), which gives v(x) = log(y(x)):
log(y(x)) = x (2 x + c_1)
Solve for y(x):
Answer: y(x) = e^(2 x^2 + c_1 x)
Answer:
The solution of differential equation is
Step-by-step explanation:
Given that,the differential equation is
It can be reframed in the given way
We use homogenous method to solve this differential equation by substituting
Substituting these in the given differential equation,we get
again
Re substituting again,
Integrating on both sides,we get
Since t is known
Therefore,the solution of differential equation is
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