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0≤x<2 ∞ y = x 2 (− 1)n x 2 n 1 2 1 (− 1)n 2 2 n ∞ e ∑ e x 4 − 2∑ ;Answer (1 of 2) Follow Ebenezer's logic as far as (x^6 2x^4y^2 x^2y^4 y^6)dy = (x^5y 2x^3y^3 xy^5)dx which I rewrite as (x⁶ 2x⁴y²
2x/y^3dx y^2-3x^2/y^4dy=0
2x/y^3dx y^2-3x^2/y^4dy=0-2 ( x 2 y 2 − 1) d y 2 x y 3 d x = 0 Let X = x 2 which leads to ( X y 2 − 1) d y y 3 d X = 0 y 3 d X d y y 2 X = 1 Considering the unknown function X ( y), this is a linear ODE It is easy to solve it The general solution is X ( y) = c y − 1 y 2 y 2 X − c y 1 = 0X to the power of 2y to the power of 3dxxy to the power of 4dy=0;
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Please Subscribe here, thank you!!!Combine all terms containing d Combine all terms containing d \left (3x^ {3}12y^ {2}x^ {2}4y^ {4}\right)d=0 ( 3 x 3 1 2 y 2 x 2 4 y 4) d = 0 The equation is in standard form The equation is in standard form \left (3x^ {3}12x^ {2}y^ {2}4y^ {4}\right)d=0 ( 3 x 3 1 2 x 2 y 2 4 y 4) d = 0Simplify (2xy)(3x^2y) Expand using the FOIL Method Tap for more steps Apply the distributive property Apply the distributive property Apply the distributive property Simplify terms Tap for more steps Simplify each term Tap for more steps Rewrite using
判定以下方程式是不是完全方程式，如果是请求解 1（2x1）dx（3y7）dy=0 2（2xy）dx（x6y）dy=0 3（5x4y）dx（4x8y的3次方）dy=0 4（sinyysinx）dx（cosxxcosyy）dy=0 5（2xy²3）dx（2x²y4）dy=0 不会的就不要乱写了 谢谢 wenjin78回答的 太对了 虽然我不会啦 但是 只有Here we will look at solving a special class of Differential Equations called First Order Linear Differential Equations First Order They are First Order when there is only dy dx, not d 2 y dx 2 or d 3 y dx 3 etc Linear A first order differential equation is linear when it can be made to look like this dy dx P(x)y = Q(x) Where P(x) and Q(x) are functions of x To solve it there is aCalculus Find dy/dx y=3x^24x y = 3x2 − 4x y = 3 x 2 4 x Differentiate both sides of the equation d dx (y) = d dx (3x2 − 4x) d d x ( y) = d d x ( 3 x 2 4 x) The derivative of y y with respect to x x is y' y ′ y' y ′ Differentiate the right side of the equation Tap for more steps
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 The Solution Of The Exact Differential Equation 2x Gauthmath | The Solution Of The Exact Differential Equation 2x Gauthmath |  The Solution Of The Exact Differential Equation 2x Gauthmath |
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 The Solution Of The Exact Differential Equation 2x Gauthmath | The Solution Of The Exact Differential Equation 2x Gauthmath |  The Solution Of The Exact Differential Equation 2x Gauthmath |
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The Solution Of The Exact Differential Equation 2x Gauthmath | The Solution Of The Exact Differential Equation 2x Gauthmath |  The Solution Of The Exact Differential Equation 2x Gauthmath |
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Problem Solve the following differential equations first finding an integrating factor $$ ( 5xy 4y^2 1 ) \, dx ( x^2 2xy ) \, dy = 0 $$ Answer I have no idea how to find an integrating factor3 Finding Z f(g(x))g′(x)dx by substituting u = g(x) Example Suppose now we wish to find the integral Z 2x √ 1x2 dx (3) In this example we make the substitution u = 1x2, in order to simplify the squareroot term We shall see that the rest of the integrand, 2xdx, will be taken care of automatically in the
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