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    Differential Equation

    Solved Problems | Topics

    Separable Ordinary Differential Equation
    ✔Obtain the general equation of \( \tan^2 y dy = \sin^3 x dx\)
    ✔Obtain the general equation of \( (1+\ln x)dx + (1 + \ln y)dy\)
    ✔Find the general solution of the equation \( xy^3 dx +e^{x^2}dy =0\)
    ✔Obtain the general solution of \( \sin x \sin y dx + \cos x \cos y dy = 0 \)
    ✔Obtain the general solution of \((1-x)y' = y^2\)
    Exact Equations
    ✔Solve the equation \( (x + 2y)dx + (2x +y ) dy = 0\)
    Homogeneous Differential Equation
    ✔Obtain a family of solutions \( (x - 2y)dx + (2x +y )dy = 0\)
    Elementary Applications
    ✔A thermometer reading is \(18^oF\) is brought into a room where the temperature is \(70^oF\); 1 min later the thermometer reading is \(31^oF\). Determine the temperature reading as a function of time and, in particular, find the temperature reading 5 min after the thermometer is first brought into the room.

    Tags: Elementary Differential Equation, Ordinary differential Equations, Separable differential Equations, Homogeneous Differential Equations, Exact Differential Equations, Linear Differential Equations, find the general solution of the given differential equation, solving differential equation, differential equation applications

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