General solution of a linear equation dy/dx + Py = Q

1. A.
   $y=\cos x+3x^2+c$
2. B.
   $y+\cos x=3x^2+c$
3. C.
   $y=3x^2\cos x+\cos x$
4. D.
   $y\cdot\cos x=3x^2+c$

Tap an option to check your answer.

1. A.
   $y(1+x^3)=x^3+c$
2. B.
   $y(1+x^3)=x+c$
3. C.
   $y(1+x^3)=x^2+c$
4. D.
   $y(1+x^3)=2x+c$

Tap an option to check your answer.

1. A.
   $xy+\cos x=\sin x+c$, where c is a constant of integration.
2. B.
   $x(y+\cos x)=\sin x+c$, where c is a constant of integration.
3. C.
   $y(x+\cos x)=\sin x+c$, where c is a constant of integration.
4. D.
   $xy+\sin x=\cos x+c$, where c is a constant of integration.

Tap an option to check your answer.

1. A.
   $y(x - 1) = x^{3} + c(x - 1)$, where $c$ is the constant of integration.
2. B.
   $y = x^{3}(x - 1) + c$, where c is the constant of integration.
3. C.
   $y(x - 1) = x^{3}(x - 1) + cx^{2}$, where $c$ is the constant of integration.
4. D.
   $y(x - 1) = x^{3}(x - 1) + c$, where c is the constant of integration.

Tap an option to check your answer.

1. A.
   $y = \cos x + \frac{2\sin x}{x} + \frac{2}{x^{2}}\cos x + \frac{x}{3}\log x - \frac{x}{9} + \frac{c}{x^{2}}$, where c is the constant of integration.
2. B.
   $\ y = - \cos x - \frac{2}{x}\sin x + \frac{2}{x^{2}}\cos x + \frac{x}{3}\log x - \frac{x}{9} + \frac{c}{x^{2}}$ where c is the constant of integration.
3. C.
   $y = - \cos x + \frac{2}{x}\sin x + \frac{2}{x^{2}}\cos x + \frac{x}{3}\log x - \frac{x}{9} + \frac{c}{x^{2}},$where $c$ is the constant of integration.
4. D.
   $y = \cos x - \frac{2}{x}\sin x + \frac{2}{x^{3}}\cos x + \frac{x}{3}\log x - \frac{x}{9} + \frac{c}{x^{2}}$ where c is the constant of intergration.

Tap an option to check your answer.

1. A.
   $y(1 + x) = x + {ce}^{x}$, where c is the constant of integration
2. B.
   $y(1 + x) = {ce}^{x}$, where c is the constant of integration
3. C.
   $y(1 - x) = x - {ce}^{x}$, where c is the constant of integration
4. D.
   $y(1 + x) = x$, where c is the constant of integration

Tap an option to check your answer.

1. A.
   $2xy - 2cx^2 - 1 = 0$
2. B.
   $2xy + 2cx^2 + 1 = 0$
3. C.
   $2xy - 2cx^2 + 1 = 0$
4. D.
   $2x^2y - 2cx + 1 = 0$

Tap an option to check your answer.

1. A.
   $x\sin x + y\cos x = c$
2. B.
   $y\sin x + x\cos x = c$
3. C.
   $xy\sin x - \cos x = c$
4. D.
   $xy\sin x + \cos x = c$

Tap an option to check your answer.

1. A.
   $1$
2. B.
   $6$
3. C.
   $4$
4. D.
   $12$

Tap an option to check your answer.

1. A.
   $\dfrac{x^4}{4} + \dfrac{5x^2}{2} - xy = c$
2. B.
   $\dfrac{x^4}{4} - \dfrac{5x^2}{2} - xy = c$
3. C.
   $\dfrac{x^4}{4} - \dfrac{5x^2}{2} + xy = c$
4. D.
   $\dfrac{x^4}{4} + \dfrac{5x^2}{2} + xy = c$

Tap an option to check your answer.

1. A.
   $y = (x + 1)(e^x + c)$
2. B.
   $y = (x + 1)(e^{-x} + c)$
3. C.
   $y = \dfrac{e^x + c}{x + 1}$
4. D.
   $y = e^x + c(x + 1)$

Tap an option to check your answer.