Number and Algebra
Functions
Geometry & Trigonometry
Statistics & Probability
Calculus
Solve the differential equation
dydx=yx+1.\frac{dy}{dx} = \frac{y}{x} + 1.dxdy=xy+1.
dydx=x−yx+y.\frac{dy}{dx} = \frac{x - y}{x + y}.dxdy=x+yx−y.
Solve the initial‐value problem
dydx=yx+2 , y(1)=3.\frac{dy}{dx} = \frac{y}{x} + 2 \;,\; y(1)=3.dxdy=xy+2,y(1)=3.
dydx=2x+3yx+2y.\frac{dy}{dx} = \frac{2x + 3y}{x + 2y}.dxdy=x+2y2x+3y.
dydx=y−2xy+2x.\frac{dy}{dx} = \frac{y - 2x}{y + 2x}.dxdy=y+2xy−2x.
dydx=3y−xy+x.\frac{dy}{dx} = \frac{3y - x}{y + x}.dxdy=y+x3y−x.
dydx=x+yx−y.\frac{dy}{dx} = \frac{x + y}{x - y}.dxdy=x−yx+y.
dydx=(yx)1/2.\frac{dy}{dx} = \biggl(\frac{y}{x}\biggr)^{1/2}.dxdy=(xy)1/2.
dydx=y2+x2xy.\frac{dy}{dx} = \frac{y^2 + x^2}{xy}.dxdy=xyy2+x2.
dydx=5x−2y3x+4y.\frac{dy}{dx} = \frac{5x - 2y}{3x + 4y}.dxdy=3x+4y5x−2y.
Solve the initial-value problem
dydx=2y−xy−2x , y(1)=2.\frac{dy}{dx} = \frac{2y - x}{y - 2x} \;,\; y(1)=2.dxdy=y−2x2y−x,y(1)=2.
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