方程\( xy'' - 5y' + 3xy = {\cos ^2}x \)的通解中包含 (写数字)个独立的任意常量。______
举一反三
- 设\(z = z\left( {x,y} \right)\)是由方程\({z^3}{\rm{ + }}3xyz - 3\sin xy = 1\)确定的隐函数，则\( { { \partial z} \over {\partial y}}=\)( ) A: \( { { y\left( {\cos xy - z} \right)} \over { { z^2} + xy}}\) B: \( { { y\left( {z - \cos xy} \right)} \over { { z^2} + xy}}\) C: \( { { x\left( {\cos xy - z} \right)} \over { { z^2} + xy}}\) D: \( { { x\left( {z - \cos xy} \right)} \over { { z^2} + xy}}\)
- 方程\( xy' + y = {e^x} \)在\( y(1) = e \)时可得通解中常量\( C = \)( )。______
- 分解因式()x()3()y()-()2()x()2()y()2()+()xy()3()正确的是A.()xy()(()x()+()y())()2()B.()xy()(()x()2()﹣()2()xy()+()y()2())()C.()xy()(()x()2()+2()xy()﹣()y()2())()D.()xy()(()x()﹣()y())()2
- \(y=x\)方程\( y - y' = 1 + xy' \)的通解。
- 下列方程中是线性微分方程的是（ ）。 A: \( \cos \left( {y'} \right) + {e^y} = x \) B: \( xy'' + 2y' - {x^2}y = {e^x} \) C: \( {\left( {y'} \right)^2} + 5y = 0 \) D: \( y'' + \sin y = 8x \)