- Webtolayers 1 1 2 X 2.5
- Webtolayers 1 1 2 X 2 1 4 Inner Tube
- 1 1/2 As A Fraction
- Webtolayers 1 1 2 X 26
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What is the solution of the Homogeneous Differential Equation? : #dy/dx = (x^2+y^2-xy)/x^2# with #y(1)=0#
1 Answer
Webtolayers 1 1 2 X 2.5
Explanation:
We have:
Which is a First Order Nonlinear Ordinary Differential Equation. Let us attempt a substitution of the form:
Differentiating wrt #x# and applying the product rule, we get:
Substituting into the initial ODE we get:
Then assuming that #x ne 0# this simplifies to:
And we have reduced the initial ODE to a First Order Separable ODE, so we can collect terms and separate the variables to get:
Both integrals are standard, so we can integrate to get:
Using the initial condition, # y(1)=0 => v(1)=0 # , we get:
Thus we have:
Duplicate photos fixer pro 2 16 tires. # -1/(v-1) = ln|x| +1 #
Webtolayers 1 1 2 X 2 1 4 Inner Tube
Then, we restore the substitution, to get the General Solution:
1 1/2 As A Fraction
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