设y1，y2是一阶线性非齐次微分方程y.+p(x)y=q(x)的两个特解，若常数λ，μ使λy1+μy2是该方程的解，λy1-μy2是该方程对应的齐次方程的解，则
A: λ=1/2,μ=1/2
B: λ=-1/2,μ=-1/2
C: λ=2/3,μ=1/3
D: λ=2/3,μ=2/3
A: λ=1/2,μ=1/2
B: λ=-1/2,μ=-1/2
C: λ=2/3,μ=1/3
D: λ=2/3,μ=2/3
举一反三
- 已知函数由下列方程确定$x^2 - y^2=1 $，则$\frac{d^2 y}{d^2 x} =$( )。 A: $\frac{1}{y^2}$ B: $-\frac{1}{y^2}$ C: $-\frac{1}{y^3}$ D: $\frac{1}{y^3}$
- 下列函数中，( )不是方程\( xy' + y - x^2 = 0 \)的解。 A: \( y = { { {x^2}} \over 3} + {1 \over x} \) B: \( y = { { {x^2}} \over 3} \) C: \( y = { { {x^2}} \over 3} + 2 \) D: \( y = { { {x^2}} \over 3} - {1 \over x} \)
- 已知点()(()-()1(),()y()1())(),()(2(),()y()2())(),()(()-()3(),()y()3())()都在函数()y()=()x()2()的图象上,则()()A.()y()1()<()y()2()<()y()3()B.()y()1()<()y()3()<()y()2()C.()y()3()<()y()2()<()y()1()D.()y()2()<()y()1()<()y()3
- 常微分方程\( y'' + y = 2{x^2} + 1 \)的阶数为（ ）. A: 1 B: 2 C: 3 D: 4
- 方程${{x}^{2}}{{y}^{''}}-(x+2)(x{{y}^{'}}-y)={{x}^{4}}$的通解是( ) A: $y={{C}_{1}}x+{{C}_{2}}{{e}^{x}}-(\frac{1}{2}{{x}^{3}}+{{x}^{2}})$ B: $y={{C}_{1}}x+{{C}_{2}}{{e}^{x}}-(\frac{1}{2}{{x}^{3}}+{{x}^{4}})$ C: $y={{C}_{1}}x+{{C}_{2}}x{{e}^{x}}-(\frac{1}{2}{{x}^{3}}+{{x}^{4}})$ D: $y={{C}_{1}}x+{{C}_{2}}x{{e}^{x}}-(\frac{1}{2}{{x}^{3}}+{{x}^{2}})$