Question
Solve the differential equations:
Answer :
Word Count : 307
We are asked to solve the differential equation: $$ \frac{dy}{dx} = -\frac{2x + y + 1}{4x + 2y - 1}. $$ First, observe that both numerator and denominator are linear in $x$ and $y$. Let's try the substitution method. Let $$ u = 2x + y. $$ Then, differentiate $u$ with respect to $x$: $$ \frac{du}{dx} = 2 + \frac{dy}{dx}. $$ From the given differential equation, $$ \frac{dy}{dx} = -\frac{2x + y + 1}{4x + 2y _______ __________ _______ ________ _____ __________ __________ ________ ____ ________ ____.
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We are asked to solve the differential equation: $$ \frac{dy}{dx} = -\frac{2x + y + 1}{4x + 2y - 1}. $$ First, observe that both numerator and denominator are linear in $x$ and $y$. Let's try the substitution method. Let $$ u = 2x + y. $$ Then, differentiate $u$ with respect to $x$: $$ \frac{du}{dx} = 2 + \frac{dy}{dx}. $$ From the given differential equation, $$ \frac{dy}{dx} = -\frac{2x + y + 1}{4x + 2y _______ __________ _______ ________ _____ __________ __________ ________ ____ ________ ____.
_____ ____ _________ ______ _____ _____ _________ ________ ______ _______.
______ ______ ________ ________ _______ __________ ___ _______.
_________ ________ ___ __________ _______ ___ _______ ___ ______ _______ ___.
________ _______ ____ _________ ____ ___ ______ _____ _______.
________ _____ ____ ___ ____ ___.
__________ __________ _____ ____ ____ ______ _______ ______ ___ _____.
_______ _________ _________ ________ ________ __________ _______ _________ ________ ____.
_______ ___ _______ ______ _________ _____ _______ ___ ______ _________ ____ _______.
________ _______ _________ _________ ___ __________ __________ ___.
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______ ___ _______ _____ ______ ___ _______ _______.
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___ _________ ____ _________ _____ _____ ______.
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