Sec 2'5: Solution by Substitutions

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Sec 2.5 Solution by Substitutions
substitution u
DE in y, x
DE in u, x
Bernoullis Equation
Case n0 , n1
linear in u
20/P78
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Sec 2.5 Solution by Substitutions
Bernoullis Equation
Step 1
Write in this form
----- (1)
Step 2
Step 3
substitute
DE is linear in u
Into (1)
Step 3
Solve linear and find u then substitute y
20/P78
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T-SHIRT
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Sec 2.5 Solution by Substitutions
Homogeneous Equation
Definition
Homogeneous function
Definition
If both M and N are homog. function with the same
degree
Homogeneous DE
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Sec 2.5 Solution by Substitutions
Homogeneous Equation
Definition
If both M and N are homog. function with the same
degree
Homogeneous DE
Separable in u, x
Separable in u, y
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Sec 2.5 Solution by Substitutions
Homogeneous Equation
Step 1
Check if homog.
Step 2
Step 3
substitute
Separable in u , x
Step 3
Solve separable and find u then substitute y
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Sec 2.5 Solution by Substitutions
Think about other DE
substitution u
DE in y, x
DE in u, x
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Sec 2.5 Solution by Substitutions
Reduction to separable
Can be reduced to separable
Separable in u, x
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Sec 2.5 Solution by Substitutions
Riccatis equation
Bernoulli
linear
Riccati
Bernoulli in u, x With n2
linear
Is particular solution
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How to solve DE
MATLAB
MATHEMATICA
gtgt dsolve('Dyy') ans C1exp(t)
DE
gtgt dsolve('Dyy','y(0)1') ans exp(t)
IVP
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Use yux if N simpler
given a particular solution
Ricatti
M N are Homog, of same degree
Use xvy if M simpler
is it linear in y
check
exact
Bernolli in y
do you have
check
is it linear in x
Made exact
substitution try something
Bernolli in x
do you have
Math 202 - 072 First Order Differential
Equations Prepared by Dr . Faisal Fairag
use
separable