• Math Archive: Questions from 2023-02-7

    Determine whether the given differential equation is exact. If it is exact, solve it. (y ln(y) - e^-xy)dx +(1/y + x lny)dy = 0

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    Determine whether the given differential equation is exact. If it is exact, solve it. (tan(x) - sin(x) sin(y))dx + cos(x) cos(y)dy = 0

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    Solve the given initial value problem (x+y)^2 dx + (2xy + x^2 - 9)dy =0 , y(1) = 1

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    Solve the given initial value problem (y^2 cos(x) - 3x^2y - 6x) dx + (2y sin(x) - x^3 + ln(y))dy = 0, y(0) = e

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    Find the value of k if the given differential equation is exact. (y^3 + kxy^4 - 2x)dx + (3xy^2 + 8x^2y^3)dy = 0

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    Solve the given differential equation by using appropriate substitution. The DE is homogeneous. (x - y)dx + xdy = 0

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    Solve the given differential equation by using appropriate substitution. The DE is homogeneous. y dx = 2(x + y) dy

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    Solve the given differential equation by using appropriate substitution. The DE is homogeneous. (y^2 + yx)dx - x^2 dy = 0

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    Solve the given differential equation by using appropriate substitution. The DE is homogeneous. -y dx + (x + sqrt(xy))dy = 0

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    Solve the given initial value problem by using appropriate substitution. The DE is homogeneous. xy^2 dy/dx = y^3 - x^3, y(1) = 4

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