Number and Algebra
Functions
Geometry & Trigonometry
Statistics & Probability
Calculus
Solve the differential equation
dydx=yx+1.\frac{dy}{dx} = \frac{y}{x} + 1.dxdyβ=xyβ+1.
dydx=xβyx+y.\frac{dy}{dx} = \frac{x - y}{x + y}.dxdyβ=x+yxβyβ.
Solve the initialβvalue problem
dydx=yx+2β β,β βy(1)=3.\frac{dy}{dx} = \frac{y}{x} + 2 \;,\; y(1)=3.dxdyβ=xyβ+2,y(1)=3.
dydx=2x+3yx+2y.\frac{dy}{dx} = \frac{2x + 3y}{x + 2y}.dxdyβ=x+2y2x+3yβ.
dydx=yβ2xy+2x.\frac{dy}{dx} = \frac{y - 2x}{y + 2x}.dxdyβ=y+2xyβ2xβ.
dydx=3yβxy+x.\frac{dy}{dx} = \frac{3y - x}{y + x}.dxdyβ=y+x3yβxβ.
dydx=x+yxβy.\frac{dy}{dx} = \frac{x + y}{x - y}.dxdyβ=xβyx+yβ.
dydx=(yx)1/2.\frac{dy}{dx} = \biggl(\frac{y}{x}\biggr)^{1/2}.dxdyβ=(xyβ)1/2.
dydx=y2+x2xy.\frac{dy}{dx} = \frac{y^2 + x^2}{xy}.dxdyβ=xyy2+x2β.
dydx=5xβ2y3x+4y.\frac{dy}{dx} = \frac{5x - 2y}{3x + 4y}.dxdyβ=3x+4y5xβ2yβ.
Solve the initial-value problem
dydx=2yβxyβ2xβ β,β βy(1)=2.\frac{dy}{dx} = \frac{2y - x}{y - 2x} \;,\; y(1)=2.dxdyβ=yβ2x2yβxβ,y(1)=2.
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