Differential Equations Answers

solve this DE :
1- X(X+Y)DY/DX=Y(X-Y)

Is the following differential equation exact or not and solve it if its exact ?


( x^2 + cosy ) + ( y^2+x+sinx) dy/dx = x

dy/dt=-y+5 y(0) =a

dear expert what are spatial variables .explain please.

dy/dx - ay = Q, where a is a constant, giving your snswer in terms of of a, when

a) Q = ke^lamda(x)
b) Q = ke^ax
c) Q = (kx^n)(e^ax)

12) use the substitution z = y^-1 to transform the differntial equation x dy/dx +y = (y^2)ln(x), into a linear equation. hense obtain the general solution of the original equation.

13) use the substitution z = y^2 to transform the differential equation 2cosx dy/dx - ysinx +y^-1 = 0, into a linear equation. hense obtain the general solution of the original equation.

14) us the substitution u = x + y to transform the differential equation dy/dx = (x +y +1)(x + y - 1) into a differential equation in u and x. by first solving this new equation. hense obtain the general solution of the original equation

15) use the substitution u = y - x - 2 to transform the differential equation dy/dx = (y - x - 2)^2 into a differntial equation in u and x. By first solving this new equation, find the general solution of the original equation, giving y in therms of x.

1.A woman is on a lake in a canoe 1km from the closest point P of a straight shoreline. She wants to get to a point Q, 10km along the shore from P. To do so, she paddles to a point R between P and Q and then walks the remaining distance to Q. She can paddle 3km/hour and walk 5km/hour. How should she pick the point R so that she gets to Q as quickly as possible?

solve the differential equation: dy/dx + y = (x+1)e^x

Dear Expert Dr math i have one problem please try to explain.Thank you
what is initial value problems and boundary vale problems.

Bacteria in a petrie dish double the area they cover everyday. If the dish is covered after 16 days, on what day was only one quarter of it covered?

I hope someone can help me with this question. Thank you very much.

"A woman 6ft tall walks away from a light 10ft above the ground. If her shadow lenghtens at the rate of 2ft/sec, how fast is she walking?"