1.设\(f(x)+2\int_{0}^{x}f(t)dt=x^{2}\)，求\(f(x)\). 查看答案[s] [p] 两端求导：\(f'(x)+2f(x)=2x\) 可得到一阶线性非齐次微分方程，...

1.求微分方程\(y'+ycosx=e^{-sinx}\)的通解. 查看答案[s] [p] \(P(x)=cosx,Q(x)=e^{-sinx}\) \(y=e^{-\int cosdx}(\int ...

1.求解下列常系数二阶方程 （1）\(y''-7y'+12y=0\). （2）\(4y''-4y'+10y=0\). （3）\(y''-2y'+y=0\). 查看答案[s] [p] （1）特征方程为：...

1.解微分方程\(\frac{dy}{dx}=2xy\). 查看答案[s] [p] 分离变量\(\frac{1}{y}dy=2xdx\) 对两端积分\(\int \frac{1}{y}dy=\int ...

直角坐标下二重积分的计算 1.计算\(\iint\limits_D(x^{2}+xy+y^{2})dxdy,D=\begin{Bmatrix} (x,y)|0\leq x\leq 1,0\leq y\...

1.验证\(x=C_{1}coskt+C_{2}sinkt\)（\(C_{1}\)、\(C_{2}\)为任意常数）是方程\(\frac{d^{2}x}{dt^{2}}+k^{2}x=0\)的通解. 查...

1.设z=ye^{sin(x+y)}，求\(\frac{\partial ^{2}z}{\partial x^{2}}\)和\(\frac{\partial ^{2}z}{\partial x \pa...

1.设\(z=z(x,y)\)由下列方程确定，求\(\frac{\partial z}{\partial x}\)和\(\frac{\partial z}{\partial y}\). （1）\(x+...

1.设\(z=u^{2}+v^{2},u=x+y,v=x-y\)，求\(\frac{\partial z}{\partial x}\)和\(\frac{\partial z}{\partial y}\...

1.求\(z=arctan(xy)\)的全微分. 查看答案[s] [p] \(\frac{\partial z}{\partial x}=\frac{1}{1+(xy)^{2}}\cdot y,\fr...