differential eqn substitution
differential eqn substitution
hey how do i solve
xy’ + y = exp(xy) using v=xy ?
ive done so far:
d/dx (xy) = exp(xy)
integrate wrt x:
xy = ∫ exp (xy) dx
then with v = xy:
v = ∫ exp(v) dx
but im not sure how you integrate exp(v) since v(x) = xy(x) so it will depend on what y(x) actually is yk. apparently it can be solved for y explicitly but i have no idea where to go from here. thanks in advance
hey how do i solve
xy’ + y = exp(xy) using v=xy ?
ive done so far:
d/dx (xy) = exp(xy)
integrate wrt x:
xy = ∫ exp (xy) dx
then with v = xy:
v = ∫ exp(v) dx
but im not sure how you integrate exp(v) since v(x) = xy(x) so it will depend on what y(x) actually is yk. apparently it can be solved for y explicitly but i have no idea where to go from here. thanks in advance
Original post by yuhyuh726329
differential eqn substitution
hey how do i solve
xy’ + y = exp(xy) using v=xy ?
ive done so far:
d/dx (xy) = exp(xy)
integrate wrt x:
xy = ∫ exp (xy) dx
then with v = xy:
v = ∫ exp(v) dx
but im not sure how you integrate exp(v) since v(x) = xy(x) so it will depend on what y(x) actually is yk. apparently it can be solved for y explicitly but i have no idea where to go from here. thanks in advance
hey how do i solve
xy’ + y = exp(xy) using v=xy ?
ive done so far:
d/dx (xy) = exp(xy)
integrate wrt x:
xy = ∫ exp (xy) dx
then with v = xy:
v = ∫ exp(v) dx
but im not sure how you integrate exp(v) since v(x) = xy(x) so it will depend on what y(x) actually is yk. apparently it can be solved for y explicitly but i have no idea where to go from here. thanks in advance
Use the substitution to get (as you have)
v' = e^v
Then you could divide through by e^v and you should recognise how you can integrate that as its just seperation of variables. Then finally replace v with xy and rearrange.
(edited 1 year ago)
Quick Reply
Related discussions
- Chemistry help a level
- A Level Maths Exam Question
- Solution by Substitution 2
- The Hydrogen Atom
- Hardest topic in A level Further Maths
- A level parametric integration question
- Deriving Euler Lagrange Equation. Stuck.
- AS-Level Maths Questions.
- Higher maths!!
- A level maths sequences and series help (again)
- Need help with why we do this.
- Integrate exponential function (two parts)
- Integration a level edexcel question
- First order differential equation
- Econ+Maths joint honours, or straight Econ?
- Integrating by substitution
- A level maths integration by parts
- Volumes of revolution question
- Best way to revise A level maths?
- Do you think A Level Maths has enough proof in it?
Latest
Trending
